As you counter opposing arguments, try to seek out one or two assumptions you might share with readers who do not initially agree with your views. If you can show that you share their concerns, your readers will be more likely to accept that your argument is valid. For example, to persuade people opposed to controlling the deer population with a regulated hunting season, a state wildlife commission would have to show that it too cares about preserving deer and does not want them to die needlessly. Having established these values in common, the commission might be able to persuade critics that reducing the total number of deer prevents starvation caused by overpopulation.
People believe that intelligence and decency support their side of an argument. To be persuaded, they must see these qualities in your argument. Otherwise, they will persist in their opposition.